The present invention provides a method and system for estimating the rate of gas production by a landfill or other subsurface body of material in which a gas flow is generated. It also provides a method for estimating the effective gas permeability of a gas generating landfill.
Estimation of the rate of landfill gas (LFG) generation is required for calculation of non-methane organic compound (NMOC) emissions under current US law, for successful design of LFG collection systems for LFG-to-energy projects, and for other LFG control systems. With respect to NMOC emissions, United States regulations allow a landfill owner to calculate emissions using a tiered approach based on estimates and/or measurements of LFG generation and NMOC concentrations within the landfill. Tiers 1 and 2 utilize a formula for LFG generation that is based in part on the size and age of the landfill and that does not involve direct measurement of LFG. Because this formula is designed to be conservative, estimates of LFG generation by this method are likely to be higher than the actual rate, especially for landfills in arid environments where low refuse moisture content may limit LFG generation. Tier 3 involves measurements from which the LFG generation rate is calculated. Similar measurement and estimation methods are typically employed to estimate LFG generation rates when designing LFG-to-energy projects and LFG control systems.
The Tier 3 methodology is generally not employed for calculation of NMOC emissions unless calculations by Tier 1 and 2 methods indicate that the NMOC emissions exceed 50 megagrams per year (MG/yr). United States regulations require the landfill owner to install an LFG control system unless the NMOC emissions calculated by Tiers 1, 2, or 3 are less than 50 MG/yr. Operation of the control system is then required until NMOC emissions drop below 50 MG/yr, which will occur eventually for a closed landfill as it ages. Periodic recalculation of NMOC emissions is required, however, to demonstrate that emissions are below this threshold, resulting in additional expense. The Tier 3 methodology is time consuming and expensive, and, as described below, does not provide a reliable estimate of the LFG generation rate or NMOC emission rate. Overestimation of LFG generation by any of these methods is costly to the landfill operator if it results in estimated NMOC emissions greater than 50 MG/yr and requires the installation of an LFG control system. Over- or under-estimation of the LFG generation rate is also costly if it results in an over- or under-designed LFG collection or control system.
The Tier 3 method involves extracting gas from a well or cluster of wells completed in landfilled materials and measuring pressure drawdown in monitoring probes completed at various depths and distances from the extraction well(s) to determine the extraction wells"" xe2x80x9cradius of influencexe2x80x9d (ROI). The Tier 3 ROI is typically taken to be the distance at which no measurable pressure drawdown occurs. Pressure drawdown is defined as the difference between xe2x80x9caverage static pressurexe2x80x9d in the landfill measured prior to gas extraction and the average pressure measured during extraction. Average pressures are used in an attempt to remove the influence of atmospheric pressure fluctuations on the measurements. The assumption is made that the xe2x80x9caverage static pressurexe2x80x9d is determinable as a reference pressure to calculate pressure drawdown after extraction begins. FIG. 1, a generalized plot of pressure versus distance from an extraction well, illustrates some of the measurements associated with the Tier 3 methodology. The pressure drop, or xe2x80x9cinfluencexe2x80x9d at a given distance from the extraction well is defined as:
I={overscore (P)}0xe2x88x92{overscore (P)}exe2x80x83xe2x80x83(1)
where
{overscore (P)}0 is the average static absolute pressure 101 (see FIG. 1) and
{overscore (P)}e is the average extraction absolute pressure 102 (see also FIG. 1)
As further seen in FIG. 1, the ROI 103 may be determined directly as the distance from the extraction well at which the measured Ixe2x89xa60 (within measurement error 104) or by extrapolating the measured I values using a semi-logarithmic regression. The accuracy of the pressure measurements is specified to be xc2x10.02 mm of mercury or 4xc3x9710xe2x88x924 pounds per square inch (psi).
Gas samples are also collected during extraction from the extraction well and monitoring probes and analyzed for nitrogen to determine whether leakage of atmospheric air into the landfill from the surface is contributing significantly to the flow to the extraction well(s). Nitrogen concentrations in excess of 20% are taken to indicate excess surface leakage. If surface leakage is not indicated by gas analysis or by negative gauge pressures in shallow monitoring probes, then the rate of gas extraction by the well(s) is assumed to be equal to the rate of LFG generation within the volume of landfill materials encompassed by the ROI. Landfill materials outside the ROI are not considered to contribute to gas flow to the extraction well.
The Tier 3 methodology rests entirely on the assumption that the gas extraction rate equals the LFG generation rate within the volume of the refuse between the extraction well and the ROI. This assumption is inconsistent with fundamental principles of gas flow to wells. To illustrate this point, assume that the LFG generation rate is uniform throughout the landfill and that the effective gas permeability of the refuse is much larger than the gas permeability of the cover so that the vertical pressure gradient in the refuse is negligible. In this case, the average difference in pressure between refuse and the atmosphere due to flow through the cover is given simply by Darcy""s Law (Al""Hussainy and others, 1966):                               q          LFG                =                                            k              c                        μ                    ⁢                                    Δ              ⁢                              xe2x80x83                            ⁢                              P                0                                                    b              c                                ⁢                      xe2x80x83                    ⁢          or                                    (        2        )                                          Δ          ⁢                      xe2x80x83                    ⁢                      P            0                          =                                            q              LFG                        ⁢                          μ              c                        ⁢                          b              c                                            k            c                                              (        3        )            
where
qLFG is the gas generation rate unit area of landfill
kc is the effective gas permeability of the cover
xcexc is the dynamic viscosity of the LFG
bc is the cover thickness
xcex94P0 is the pressure differential P0xe2x88x92Pa 
Pa is the atmospheric pressure
P0 is the pressure in the refuse.
Given the assumption of a uniform LFG generation rate and an areally extensive landfill, the static pressure in the refuse is
{overscore (P)}0={overscore (P)}a+xcex94P0xe2x80x83xe2x80x83(4)
where {overscore (P)}a is the average atmospheric pressure. Given the assumptions above, {overscore (P)}0 is uniform throughout the landfill.
For small pressure differentials, the pressure drop created by an extraction well (assuming an ideal gas and steady-flow conditions and ignoring compressibility effects) is given by:                               Δ          ⁢                      xe2x80x83                    ⁢                      P            e                          =                                                            -                                  Q                  e                                            ⁢              μ                                      2              ⁢              π              ⁢                              xe2x80x83                            ⁢                              k                r                            ⁢                              b                r                                              ⁢                      P            D                                              (        5        )            
where
kr is the effective horizontal gas permeability of the refuse,
Qe is the well extraction rate,
PD is an appropriate dimensionless pressure solution for flow to the well,
xcex94Pe is the difference between static and flowing pressure, and
br is the thickness of the refuse.
For the case of a well fully penetrating a highly permeable refuse in a lined landfill with a relatively low permeability cover, the appropriate PD function is that given by Hantush (1964) for a leaky, confined formation without fluid storage in the confining bed:                                           P            D                    =                                    K              0                        ⁡                          (                              r                /                B                            )                                      ;                  B          =                                    (                                                                    k                    r                                    ⁢                                      b                    r                                    ⁢                                      b                    c                                                                    k                  c                                            )                                      1              /              2                                                          (        6        )            
where K0 is the modified Bessel function of zero order.
Thus, equation (5) becomes                               Δ          ⁢                      xe2x80x83                    ⁢                      P            e                          =                                                            -                                  Q                  e                                            ⁢              μ                                      2              ⁢              π              ⁢                              xe2x80x83                            ⁢                              k                r                            ⁢                              b                r                                              ⁢                                    K              0                        ⁡                          (                              r                /                B                            )                                                          (        7        )            
The average absolute pressure within the refuse during extraction is then
{overscore (P)}e={overscore (P)}0+xcex94Pexe2x80x83xe2x80x83(8)
The generalized absolute pressure in the refuse 102 based on (7) is illustrated in FIG. 1 along with its relationship to the static pressure 101. In the Tier 3 methodology, the ROI 103 is defined as the radial distance from the extraction well at which the difference between the absolute pressure during extraction and the static absolute pressure is zero, that is,
{overscore (P)}0xe2x88x92{overscore (P)}e=0xe2x80x83xe2x80x83(9)
within measurement error 104. Using the Tier 3 criteria, the following assumption is made:                                           Δ            ⁢                          xe2x80x83                        ⁢                          P              e                                ≅          0                =                                                            -                                  Q                  e                                            ⁢              μ                                      2              ⁢              π              ⁢                              xe2x80x83                            ⁢                              k                r                            ⁢                              b                r                                              ⁢                                    K              0                        ⁡                          (                                                r                  e                                /                B                            )                                                          (        10        )            
where re is the radius of influence.
Equations (8) and (10) and FIG. 1 illustrate two problems with the Tier 3 approach. First, although the pressure drop induced by the extraction well approaches zero as r increases (K0xe2x86x920 as rxe2x86x92∞), it never actually reaches zero and the radius of influence depends on the measurement error. The larger the error, the less the radius of influence and vice-versa. Second, and more importantly, the LFG generation rate plays no role in equation (7) so that the distance (re) at which xcex94Pe is zero within measurement error is independent of the LFG generation rate. Therefore, the LFG generation rate cannot be determined using the Tier 3 methodology.
Additional analysis of the xe2x80x9cradius of influencexe2x80x9d (i.e. Tier 3) methodology, as well as other LFG collection methodologies is provided by U.S. Pat. No. 5,063,519. The ""519 patent offers as a solution a methodology in which measurements of the effective gas permeability of the landfill cover soil are made independent of the landfill gas pressure measurements by determining soil permeability from soil samples that are collected over the time period of the test. In the ""519 patent the tester is advised to avoid inserting the probe (pressure measuring device) into the refuse portion of the landfill. The tester uses the permeabilities and their spatial variability, the pressure data and its spatial variability, and other data to calculate the cumulative frequency distribution of LFG flow through the landfill surface. Moreover, in the methodology of the ""519 patent, it is assumed that all of the gas generated within the landfill leaves the landfill through the soil cover (except for that which may be extracted by wells).
The present invention provides a new and useful method and system for estimating LFG generation in a way that is relatively inexpensive, efficient to perform, and which is designed to improve the accuracy of the gas generation estimate.
With the present invention, the landfill conditions that require a landfill operator to install an LFG control system can be more accurately estimated than with the Tier 3 methodology, thus minimizing the likelihood that an LFG control system will be unnecessarily required for the landfill. In the case of a LFG-to-Energy project, the energy production potential of the landfill can be more accurately estimated and the profitability of the project can be enhanced.
Moreover, unlike the methodology of the ""519 Patent, the methodology of the present invention uses the atmospheric and landfill pressures to estimate both the landfill permeability and the LFG generation rate, rather than requiring soil samples to be collected and analyzed to determine soil permeability (as in the ""519 patent). Additionally, whereas the methodology of the ""519 patent assumes that all of the gas generated within the landfill leaves the landfill through the soil cover (except for that which may be extracted by wells), and requires that the gas pressure measurements be taken from the soil cover (but not the gas generating refuse), the methodology of the present invention recognizes that in the case of unlined landfills, some of the gas will leave the landfill through the soil which supports the landfill and provides gas pressure measurements that are taken within the refuse portion of the landfill, and under certain conditions in the supporting soil below or to the side of the gas generating refuse portion of the landfill.
According to the present invention, the gas generation rate in a portion of a landfill is estimated by obtaining a time history record of atmospheric pressure that is representative of atmospheric pressure at a surface boundary of the landfill, measuring the gas pressure at least at one selected subsurface location at the landfill site over a time period that is included in the time history record, and using the atmospheric pressure and the measured gas pressure over the time period to estimate the LFG generation rate of the portion of the landfill.
In a preferred embodiment, gas pressure is measured at a surface boundary of the landfill and at a plurality of selected locations within the gas generating refuse portion of the landfill, and in the case of an unlined landfill in the supporting soil below (and in some cases on the side of) the landfill, and the measured pressures are used to estimate the LFG generation rate of the landfill.
The invention recognizes that the rate of landfill gas generation from a landfill, e.g. a municipal solid waste landfill, can be determined with reasonable engineering accuracy by measuring gas pressure within and at the surface of the landfill (and in the case of an unlined landfill gas pressure below and to the side of the landfill) and analyzing its response to changes in atmospheric pressure.
Moreover, the principles of the present invention can be used to estimate the gas permeability of a portion of a gas generating landfill independent of determining the gas generation rate.
Other features of the present invention will become apparent from the following detailed description and the accompanying drawings.